Analysis of the Capture Probability in Wireless Systems with Multi-Packet Reception Capabilities and Successive Interference Cancellation

In this paper, we address the problem of computing the probability that r out of n interfering signals can be correctly received in a random access wireless system with capture, capable of performing up to K successive interference cancellation iterations. We provide an expression for the probability distribution of the number of captured packets that is scalable with n and r. We also provide an approximate expression for the mean number of captured signals, which gives the system throughput as a function of K and n. The approximation is much easier to compute than the exact mean and provides good results for reasonable values of K. Finally, we present some selected results for a case study with the purpose of illustrating the potential of the proposed mathematical framework, and validate the accuracy of the approximate method for the computation of the system throughput.